Many geographers are familiar with ArcGIS, QGIS, and other 'software suites' that have become the de facto standard in both academia and industry. Less often however, are we given opportunity (or challenge) to investigate the core tenets of geographic information science; the following widgets have been my personal effort to understand and apply these tenets.
Minimum Bounding Geometries
Many basic analyses of points rely on an estimate of the area occupied by the set; consider the simplest estimate of point density (the number of points given a defined area, or mathematically = n/A
But how do we determine the Area, A? Many GIS tools might default to using a Convex Hull, but that's not the only option available to the geo-statistician:
Nearest Neighbors, and the Nearest Neighbor Index
Among the basic point-feature analyses is 'nearest neighbors' -- the simple idea is, for each point, to identify the next nearest point; typically, this includes reporting these pairs, their distance from each other, and finally, the average nearest neighbor distance. We often extend the idea of nearest neighbors one step further, using this 'average' to compare the observed point density to a theoretical, expected random sample; there's only one caveat: the analysis demands an estimate of area!
One other aspect introduced by the nearest neighbors' analyses is the neighborhood, or distance matrix -- a table that shows the relationship between each single point and every other point. We can extend this a bit further too: how do express the strength of a relationship between points? One traditional method is the inverse distance matrix...